Ohm's law (microscopic interpretation)

         

Suppose that the number of conduction electrons per unit volume in a certain metal is n=1.23×1029 m3n=1.23 \times 10^{29} \text{ m}^{-3} and the mean free time between collisions for the conduction electrons in that metal is τ=3.42×1015 s.\tau=3.42 \times 10^{ -15} \text{ s}. What is the resistivity ρ\rho of that metal?

The elementary charge is e=1.60×1019 Ce=1.60 \times 10^{-19}\text{ C} and the mass of electron is m=9.11×1031 kg.m=9.11 \times 10^{-31}\text{ kg}.

If the number of conduction electrons per unit volume in copper is 8.47×1028 m38.47 \times 10^{28}\text{ m}^{-3} and the resistivity of copper is 1.61×108Ωm,1.61 \times 10^{-8}\,\Omega\cdot\text{m}, what is the mean free time τ\tau between collisions for the conduction electron in copper?

The elementary charge is e=1.60×1019 Ce=1.60 \times 10^{-19}\text{ C} and the mass of electron is m=9.10×1031 kg.m=9.10 \times 10^{-31}\text{ kg}.

If the mean free time between collisions for the conduction electrons in copper is τ=2.5×1014 s\tau=2.5 \times 10^{-14}\text{ s} and their effective speed veffv_{\text{eff}} is 1.5×106 m/s,1.5 \times 10^6\text{ m/s}, what is the mean free path λ \lambda for the conduction electron in copper?

The measured resistivity of aluminium at 25C25\,^\circ\text{C} is 2.72×108Ωm.2.72 \times 10^{-8}\,\Omega\cdot\text{m}. The valency, density, and the atomic mass of aluminium are 3,3, 2.68g/cm3,2.68\text{g/cm}^3, and 27,27, respectively. Assuming that each aluminium atom contributes three free conduction electrons to the metal, what is the mean free time between collisions for the conduction electrons in aluminium at a temperature of 25C?25\,^\circ\text{C}?

The elementary charge is e=1.602×1019 C.e=1.602 \times 10^{-19}\text{ C}.
The mass of electron is m=9.109×1031 kg.m=9.109 \times 10^{-31}\text{ kg}.
The Avogadro constant is NA=6.022×1023 mol1.N_A=6.022 \times 10^{23}\text{ mol}^{-1}.

The measured electron drift mobility in silver is 57 cm2V1s157\text{ cm}^2\text{V}^{-1}\text{s}^{-1} at 27C.27\,^\circ\text{C}. The atomic mass and density of silver are 107.87 g/mol107.87\text{ g/mol} and 10.70 g/cm3,10.70\text{ g/cm}^3, respectively. Assuming that each silver atom contributes one conduction electron, what is the resistivity of Ag at 27C?27\,^\circ\text{C}?

The elementary charge is e=1.602×1019 C.e=1.602 \times 10^{-19}\text{ C}.
The mass of electron is m=9.109×1031 kg.m=9.109 \times 10^{-31}\text{ kg}.
The Avogadro constant is NA=6.022×1023 mol1.N_A=6.022 \times 10^{23}\text{ mol}^{-1}.

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